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Postselection based on measurement results can lead to nonlinear transformations of initial quantum states. The iteration of such schemes on an ensemble of qubits leads to a dynamics that is very sensitive to the initial qubit state and the final state can get very far from the initial state after a few iterational steps already. I will show an experimentally realizable scheme where we showed that the emerging nonlinear transformation is capable of orthogonalizing quantum states that are initially highly overlapping. The orthogonalized states can then be distinguished by a projective measurement, therfore the scheme could be used for quantum state discrimination [1]. I will present a class of such nonlinear transformations that could be used for the same purpose and show that among these, there are transformations which are capable of deciding whether an unknown pure qubit state is in a predefined neighborhood of a reference state or not. We called this quantum informational task „quantum state matching". I will show that one can construct an appropriate nonlinear transformation for any reference state and for any neighborhood, and that a corresponding two-qubit unitary transformation can be determined with which such transformations could be implemented [2].
[1] J. M. Torres, J. Z. Bernád, G. Alber, O. Kálmán, T. Kiss, Phys. Rev. A 95, 023828 (2017).
[2] O. Kálmán, T. Kiss, Phys. Rev. A 97, 032125 (2018).